Introduction to Statistics
Part A- Outputs:
1. A sample of university employees had been assembled. An output concerning their education is presented below. Study the output and answer the following questions:
a. What is the mean, median and the standard deviation?
b. Firstly, what is the interquartile range, and secondly, how many education years has the most educated employee?
c. What is the number of education years that 36% of the sample has that number of education years or below it? Answer the same question for 83%.
d. Firstly, how many employees has 12 education years or less? Secondly, how many employees have missing values in the variable education years?
Statistics
Highest Year of School Completed
|
N
|
Valid
|
1510
|
|
|
Missing
|
7
|
|
Mean
|
|
12.88
|
|
Median
|
|
12.00
|
|
Mode
|
|
12
|
|
Std. Dev iation
|
|
2.984
|
|
Variance
|
|
8.904
|
|
Range
|
|
20
|
|
Minimum
|
|
0
|
|
Maximum
|
|
20
|
|
Sum
|
|
19455
|
|
Percentiles
|
10
|
9.00
|
|
|
25
|
12.00
|
|
|
36
|
12.00
|
|
|
50
|
12.00
|
|
|
75
|
15.00
|
|
|
83
|
16.00
|
Highest Year of School Completed
| |
Frequency
|
Percent
|
Valid Percent
|
Cumulativ e Percent
|
|
Valid
|
0
|
2
|
.1
|
.1
|
.1
|
|
|
3
|
5
|
.3
|
.3
|
.5
|
|
|
4
|
5
|
.3
|
.3
|
.8
|
|
|
5
|
6
|
.4
|
.4
|
1.2
|
|
|
6
|
12
|
.8
|
.8
|
2.0
|
|
|
7
|
25
|
1.6
|
1.7
|
3.6
|
|
|
8
|
68
|
4.5
|
4.5
|
8.1
|
|
|
9
|
56
|
3.7
|
3.7
|
11.9
|
|
|
10
|
73
|
4.8
|
4.8
|
16.7
|
|
|
11
|
85
|
5.6
|
5.6
|
22.3
|
|
|
12
|
461
|
30.4
|
30.5
|
52.8
|
|
|
13
|
130
|
8.6
|
8.6
|
61.5
|
|
|
14
|
175
|
11.5
|
11.6
|
73.0
|
|
|
15
|
73
|
4.8
|
4.8
|
77.9
|
|
|
16
|
194
|
12.8
|
12.8
|
90.7
|
|
|
17
|
43
|
2.8
|
2.8
|
93.6
|
|
|
18
|
45
|
3.0
|
3.0
|
96.6
|
|
|
19
|
22
|
1.5
|
1.5
|
98.0
|
|
|
20
|
30
|
2.0
|
2.0
|
100.0
|
|
|
Total
|
1510
|
99.5
|
100.0
|
|
|
Missing
|
NA
|
7
|
.5
|
|
|
|
Total
|
|
1517
|
100.0
|
|
|
2. Researcher which studies the field of eating disorders checked the correlation between subject's body image ranking and the degree to which they restrict food intake. Study the output and answer the following questions:
|
|
Body perception
|
Restriction of f ood intake (f asting)
|
|
Body perception Pearson Correlation
|
1
|
.383**
|
|
Sig. (2-tailed)
|
|
.000
|
|
N
|
217
|
217
|
|
Restriction of f ood Pearson Correlation
|
.383**
|
1
|
|
intake (f asting) Sig. (2-tailed)
|
.000
|
|
|
N
|
217
|
217
|
1. What can be inferred from the table?
a. There is a significant negative correlation between the variables.
b. There is a moderately negative correlation between the variables.
c. There is a moderately positive correlation between the variables.
d. There is a weak positive correlation between the variables.
2. Report the correlation.
3. The following output present a regression done in order to predict the number of SMS messages a person sends to his\hers partner by the length of the relationship (in years). Study the output and answer the following questions:
Regression
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
-.661(a)
|
.436
|
.435
|
123.540
|
a. Predictors: (Constant), Duration of relationship (years)
ANOVA(b)
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
6010.000
|
1
|
100.000
|
365.381
|
.000(a)
|
|
|
Residual
|
7776.340
|
472
|
160.840
|
|
|
Total
|
13776.340
|
473
|
|
a. Predictors: (Constant), Duration of relationship (years) b Dependent Variable: SMS
Coefficients(a)
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
|
|
B
|
Std. Error
|
Beta
|
B
|
Std. Error
|
|
1
|
(Constant)
|
15.178
|
2821.912
|
.661
|
-6.496
|
.000
|
|
|
Duration of relationship (years)
|
-0.183
|
204.547
|
19.115
|
.000
|
a. Dependent Variable: SMS
1. What is the percentage of explained variance?
2. Write the regression line equation.
3. Brad and Angelina are married for 25 years. According to this analysis, how many SMS messages should Brad send Angelina?
4. A researcher is conducting a research on the effects of sociability on mood. He is using a questionnaire in order to assess sociability. Study the output concerning the reliability check and answer the following questions:
Reliability
Scale: sociability
Case Processing Summary
|
|
N
|
%
|
|
|
Valid
|
198
|
99.0
|
|
Cases
|
Excludeda
|
2
|
1.0
|
|
|
Total
|
200
|
100.0
|
a. Listwise deletion based on all variables in the procedure.
Reliability Statistics
|
Cronbach's Alpha
|
Cronbach's Alpha Based on Standardized Items
|
N of Items
|
|
.627
|
.659
|
8
|
Inter-Item Correlation Matrix
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
1. I like to see friends
|
1.000
|
.605
|
-.024
|
.189
|
.501
|
-.435
|
.451
|
.396
|
|
2. I talk a lot with friends on the phone
|
.605
|
1.000
|
-.001
|
.362
|
.492
|
-.837
|
.509
|
.424
|
|
3. I like chocolate
|
-.024
|
-.001
|
1.000
|
.003
|
.009
|
.001
|
-.001
|
-.017
|
|
4. I go to a lot of parties
|
.189
|
.362
|
.003
|
1.000
|
.408
|
-.557
|
.430
|
.411
|
|
5. I have many friends
|
.501
|
.492
|
.009
|
.408
|
1.000
|
-.243
|
.675
|
.510
|
|
6. I like to read alone at home
|
-.435
|
-.837
|
.001
|
-.557
|
-.243
|
1.000
|
-.408
|
-.650
|
|
7. Romantic relationship are important
|
.451
|
.509
|
-.001
|
.430
|
.675
|
-.408
|
1.000
|
.495
|
|
8. I feel good with my social status
|
.396
|
.424
|
-.017
|
.411
|
.510
|
-.650
|
.495
|
1.000
|
Item-Total Statistics
| |
Scale Mean if Item Deleted
|
Scale Variance if Item Deleted
|
Corrected Item- Total Correlation
|
Squared Multiple Correlation
|
Cronbach's Alpha if Item Deleted
|
|
1. I like to see friends
|
17.4495
|
26.188
|
.515
|
.443
|
.561
|
|
2. I talk a lot with friends on the phone
|
17.2374
|
24.009
|
.555
|
.472
|
.534
|
|
3. I like chocolate
|
16.1919
|
29.811
|
.007
|
.018
|
.686
|
|
4. I go to a lot of parties
|
15.9697
|
23.826
|
.399
|
.330
|
.571
|
|
5. I have many friends
|
16.7273
|
21.753
|
.666
|
.546
|
.489
|
|
6. I like to read alone at home
|
14.6768
|
35.540
|
-.320
|
.196
|
.753
|
|
7. Romantic relationship are important
|
17.0556
|
23.220
|
.634
|
.528
|
.512
|
|
8. I feel good with my social status
|
16.4192
|
23.260
|
.473
|
.397
|
.547
|
1. What is the number of subjects whose answers had been entered to the reliability check?
2. What is the internal reliability of the sociability questionnaire?
3. Which item (or items) would you suggest to change or omit (leave out)? Explain why, both from a statistical point of view and from the theoretical point of view.
Part B - statistical comprehension:
1. Study the table and answer the following questions:
Taken from Somer, E., Maguen, S., Or-Chen, K. & Litz, B. (2008). Managing Terror: Differences between Jews and Arabs in Israel. International Journal of Psychology, 42, 1-9.
Table 1
Demographic Variables of Jewish-Israelis and Arab-Israelis
|
Demographic Characteristics
|
Jewish- Israelis
(n = 100)
|
Arab- Israelis
(n = 100)
|
Statistic comparing the two groups
|
|
|
M = 43.60
(SD = 16.76)
|
M = 36.62 (SD=13.02)
|
t(198) = 10.82**
|
|
Age (years)
|
|
|
Gender
Male
Female
|
24%
76%
|
34%
66%
|
χ2 = 2.43
|
|
Marital status
Married
Non-Married
|
60%
40%
|
73%
27%
|
χ2 = 3.79
|
|
Religion
Jewish
Christian
Muslim
Druze
|
100%
0%
0%
0%
|
0%
72%
27%
1%
|
χ2 = 200**
|
Table 1
Demographic Variables of Jewish-Israelis and Arab-Israelis
|
Demographic Characteristics
|
Jewish- Israelis
(n = 100)
|
Arab- Israelis
(n = 100)
|
Statistic comparing the two groups
|
|
Religiosity
Religious
Traditional
Seculra
|
10%
26%
64%
|
18%
58%
24%
|
χ2 = 32.66**
|
|
Birthplace
Israel
Other
|
60%
40%
|
99%
1%
|
χ2 = 46.66**
|
*p<0.05
**p<0.01
1. What is the conclusion from the results of the test done between nationality and age? Did a significant correlation had been found? Which test did the researchers use?
2. The Pearson correlation between all the of the research variables is displayed in the following table. Please report (in length) what is the most important correlation. explain why.
Table 2
Correlations Among Variables in Regression Models
|
Variable
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
1. PTSD
|
--
|
|
|
|
|
|
|
|
|
|
|
2. Depression
|
.77**
|
--
|
|
|
|
|
|
|
|
|
|
3. Somatization
|
.58**
|
.66**
|
--
|
|
|
|
|
|
|
|
|
4. Group
|
-.38**
|
-.46 **
|
-.04
|
--
|
|
|
|
|
|
|
|
5. Age
|
.03
|
-.03
|
.19**
|
.23**
|
--
|
|
|
|
|
|
|
6. Gender
|
.21**
|
.23**
|
.20**
|
.11
|
.05
|
--
|
|
|
|
|
|
7. Education
|
-.22**
|
-.23**
|
-.27**
|
.16*
|
.06
|
-.05
|
--
|
|
|
|
|
8. Religiosity
|
-.20**
|
-.21**
|
-.09
|
.34**
|
.10
|
-.03
|
-.26**
|
--
|
|
|
|
9. Marriage
|
-.13
|
-.12
|
-.09
|
.14
|
-.47**
|
-.04
|
.05
|
.15*
|
--
|
|
|
10. Birthplace
|
-.15
|
-.21**
|
.02
|
.48**
|
.45**
|
.11
|
.08
|
.19**
|
-.07
|
--
|
*p<0.05
**p<0.01